为了提高光笔式三坐标视觉测量的正确性和有效性, 对六点透视问题的理论渊源、数学模型及其数学模型的正确性和有效性进行了研究。以视觉测量的经典理论——“N点透视问题”的原理为依据, 建立了光笔式三坐标视觉测量的通用数学模型。在充分分析和研究该通用数学模型解的性态的基础上, 得出了光笔式三坐标视觉测量中的六点透视问题具有唯一解, 而且可线性求解的结论, 建立了六点透视问题的数学模型, 并开发出对应该数学模型的实验测量系统, 在三坐标测量机上进行了比对测量实验。比对测量结果表明: 在300mm 测量范围内, 六点透视问题实验测量系统和三坐标测量机在X、Y、Z轴方向上的测量数据最大差值分别为0.06mm、0.07mm和0.09mm。六点透视问题的数学模型能基本满足现场测量精度的要求。

In order to improve the correctness and validity for three coordinate vision measurement using a light-pen, the origin, mathematic model and its correctness and validity of “six-point perspective problem” are studied. According to the classical “N-point perspective problem” theory, the universal mathematic model is established for three coordinate vision measurement using a light-pen. On the basis of analyzing and studing the solutions of the above universal mathematic model, a conclusion is drawn that “six-point perspective problem” has a unique solution and can be solved linearly in three coordinate vision measurement using a light-pen, and the mathematic model for “six-point perspective problem” is established. Finally, the experiment measuring system for “six-point perspective problem” is developed, and the comparing measuring experiment is conducted on the Coordinate Measuring Machine(CMM). The comparing measurement result shows that the maximum difference value between the measuring data of the “six-point perspective problem” experiment system and CMM is 0.06mm, 0.07mm and 0.09mm in 300mm measuring range along the X, Y, Z axis respectively, which meets the requirement of the measuring accuracy basically on spot.